wirral...glad to hear from you. Thanks for clarifying, and happy to help. I don't think you will feel daft at all, as I bet you will see lots of single moms and dads out with their children. If not at the specific place you go to, no one will give you a second glance so not to worry.
The UK being unfriendly to children at night is an understatement. DH and I had no idea kids were so hated here. Our families don't even want to visit us here anymore because kids are so hated. We all enjoy dining out, so we usually meet friends/family on the Continent. We all rent a villa together and enjoy lots of nice dinners out, or we just get together when we go back to the States.
Why is England so bad with kids?..I mean I have a problem with poorly behaved kids, but why can't children with manners go out to nice restaurants with their parents? Is Scotland also so bad? A lot of people tell us that we'll love Scotland and DH's grandmother is from there, but then other people tell us it's just like England. We love France, Spain and Italy and they don't hate kids there. We've actually made reservations for three..only to not be allowed to dine when they find out DD is the third person. Unbelievable!
There are lots of things to do in the states with kids at night. You might be interested in one of those miniature golf places (they call it putt-putt golf). Yes, they are somewhat silly, but well lit up at night and your daughter will probably love it. There are lots of family-oriented places to go..in fact you will be hard pressed to find places that don't allow kids.
I would definitely read lots of books and visit websites...visit US sites, not just UK ones and you will know they don't hate kids. Also, read up about driving. For example, you can turn right on red in the US aafter coming to a complete stop beforehand(well states are different, but it's ok in FL) unless there's a sign specifically prohibiting it. Also, there's usually a stop sign when entering one street from another, and stop means stop just like here. The police love to give tickets when for half-*aa stops.
I would be careful of getting real chummy with strangers that you just meet places. It might be okay, but might not be. (Maybe this is just my own worry, but I'm suspicious when people are too friendly too quickly and I'm American and still think this.) Obviously, if you meet someone at your hotel pool or something and you're sure they really ARE staying at the same hotel, you will probably meet lots of people from all over travelling. I just wouldn't give out details about where you're staying or anything. I'm sure you wouldn't do this anyway.
Also, use the A/C in your hotel room if necessary and do not leave the door open, even if you're in the room. Read in the US media about all the people who get mugged (usually the English) in their rooms while they're inside. They leave the door open to get fresh air and have good intentions of saving the environment, but Americans would never do this..even in their own home. So please close the door, and if it gets warm, just turn the a/c on. Aparently, a lot of English and a few Germans were mugged and the hotel couldn't understand why anybody would be so stupid as to leave their door open. I'm green conscious too, but don't do this...not that you would while alone.
Finally, yes I have travelled alone with a child to places where they don't speak English (Korea) and this bit is what scares me ...just did lots of research...even to the point that I knew instantly if the cab driver was taking the long way to the hotel to charge a higher fare.
Good luck and have fun!